# Trigonometry Part 8: Advance maths important questions.

## Trigonometry Part 8: Advance maths important questions.

Trigonometry Part 8: Advance maths important questions.

Q281. If cosec A = 2 then

(a) 2

(b) 5

(c) 4

(d) 1

Q282. The angle of elevation of tower at a point is such that the value of its tan is  on moving 240m towards the tower its value of tan of angle fo elevation becomes  Then the height of the tower is:

(a) 220 m

(b) 200 m

(c) 225 m

(d) 240 m

Q283. The minimum value of 2sin2θ+3cos2θ is

(a) 0

(b) 3

(c) 2

(d) 1

Q284. If cosec 39° = x, the value  of

(a)

(b)

(c)   x2– 1

(d) 1 – x2

Q285. The value of tan 4° tan 43° . tan 47°. tan 86° is

(a) 2

(b) 3

(c) 1

(d) 4

Q286.

(a)   2/√3

(b)   √3/2

(c)     1/2

(d)     1

Q287.  If cos x + cos y = 2, the value of sin x + sin y is :

(a) 0

(b) 1

(c) 2

(d) -1

Q288.  The value of tan 1° tan 2° tan 3°…..tan 89° Is :

(a) 1

(b) 0

(c) √3

(d) 1/√3

Q289.  The measure of the angles of a triangle are in the ration 2 : 7 : 11. Measures of angles are :

(a)   16° 56° 88°

(b)   18° 63° 99°

(c)   20° 70° 90°

(d)   25° 175° 105°

Q290.  The angles of a triangle are (x+5)°, (2x-3)° and (3x+4)°. The value of x is

(a) 30

(b) 31

(c) 29

(d) 28

Q291. The value of cot 10°. Cot 20° cot 60°. Cot .70°.cot 80° is :

(a)    1

(b)   -1

(c)   √3

(d)  1/√3

Q292. If  θ be an acute angle and 7 sin θ + 3cos θ= 4, then the value of tan θ is:

(a) √3

(b) 1/√3

(c) 1

(d) 0

Q293. The value of sin21° + sin25° + sin29° + …+ sin289° is

(a)

(b) 11√2

(c) 11

(d) 11/√2

Q294. The numerical value of cot18°  is

(a) 1

(b)  √2

(c) 3

(d) 1/√3

Q295.   If tan 15°= 2 – √3, the value of tan 15° cot 75° + tan 75° cot 15° is

(a) 14

(b) 12

(c) 10

(d) 8

Q296. If x, y are acute angles, 0 < x + y < 90° and sin (2x – 20°) = cos (2y + 20°), then the value of tan (x + y) is :

(a)  1/√3

(b)

(c)  √3

(d)     1

Q297.  If  ΔA and ΔB are complementary to each other, then the value of sec2 A + sec2 B – sec2 A.  sec2 B is :

(a) 1

(b) -1

(c) 2

(d) 0

Q298.  sin2 5° + sin26° +…+ sin284° + sin285° = ?

(a)

(b)

(c)     40

(d)

Q299.  sin25° + sin210° + sin2 15° + …+ sin285° + sin2 90° is equal to

(a)

(b)

(c)    9

(d)

Q300. The value of + 2 tan 11° tan 31°  tan 45° tan 59° tan 79°- 3(sin221°+ sin2 69°) is :

(a)  2

(b) -1

(c)  1

(d) 0

Q301.

(a)  30°

(b)  45°

(c)  60°

(d)  None of these

Q302. If A = tan 11° tan 29° ,  B = 2 cot 61° cot 79°  then :

(a) A = 2B

(b) A = -2B

(c) 2A = B

(d) 2A= – B

Q303. .  If sin 17°=   , then the value of (sec 17° – sin 73°) is :

(a)

(b)

(c)

(d)

Q304. If 0°<θ< 90°, then value of sin θ  + cos θ is

(a) equal to 1

(b) greater than 1

(c) less than  1

(d) equal to 2

Q305.  The expression   is equal to

(a) tan 33° cot 57°

(b) tan 57° cot 37°

(c) tan 33° cot 53°

(d) tan 53° cot 37°

Q306. The value of    is:

(a) 0

(b) 1

(c) √3-1

(d) -1

Q307. The value of cot θ. tan (90°- θ) – sec (90°- θ) cosec θ + (sin225° + sin2 65°) +√3 (tan 5° tan 15°. tan 30°. tan 75°. tan 85°) is :

(a) 1

(b) -1

(c) 2

(d) 0

Q308.   if sin (3x-20°) = cos (3y+20°), then the value of (x+y) is

(a) 20°

(b) 30°

(c) 63°

(d) 67°

Q309. If cosθ cosec 23° = 1, the value of θ  is :

(a) 23°

(b) 37°

(c) 63°

(d) 67°

Q310. .  If 2(cos2θ – sin2θ) = 1, θ  is a positive acute angle, then the value of θ is

(a)

(b)  30°

(c) 45°

(d) 60°

Q311. the value of (tan35° tan 45° tan 55°) is :

(a) 1/2

(b) 2

(c) 0

(d) 1

Q312.  If sec (7θ + 28°) = cosec (30°-3θ) then the value of θ  is :

(a) 8°

(b) 5°

(c) 60°

(d) 9°

Q313.  If tan =√3 , the value of cos is

(a)     0

(b)    1/√2

(c)   1/2

(d)    1

Q314.  If 7 sin2 θ+3 cos2  θ= 4(0°≤θ≤ 90°), then value of θ is :

(a) π/2

(b) π/3

(c) π/6

(d) π/4

Q315. If  (0°<θ< 90°), then sec θ  + tan θ is equal to

(a) x/2

(b) 2x

(c) x

(d) 1/2x

Q316. The value of cos 1° cos 2° cos 3°……cos 177° cos 178° cos 179° is :

(a) 0

(b) 1/2

(c) 1

(d) 1/√2

Q317.  The value of (sin2 25° + sin265°) is :

(a) √3

(b)   1

(c)   0

(d) 2/√3

Q318. If sec θ + tan θ =√3-(0≤θ≤90°), then tan 3θ is :

(a) undefined

(b) 1/√3

(c) √3

(d) 1

Q319. If sin (60° – θ) = cos(Ψ-30°) then the value of tan (Ψ- θ) is (assume that θ are both positive acute angles with θ< 60° and Ψ> 30°).

(a)  1/√3

(b)  0

(c)  √3

(d)  1

Q320. If a sin θ  + b cos θ = c then the value of a cos θ – b sin θ is

(a)

(b)

(c)

(d)

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